File:Burning Ship Fractal Zoom.png

A view of the Burning Ship fractal. This is a fractal generated by iterating the following equation for each point with coordinates c in the complex plane:

${\displaystyle Z_{n+1}=\left(|\Re \left({Z_{n}}\right)|-i|\Im \left({Z_{n}}\right)|\right)^{2}+c,\quad Z_{0}=0}$

This image is in the complex plane with lower left corner (-1.8, -0.02i) and upper right corner (-1.7, 0.055i). Some descriptions of this fractal give the equation with an addition rather than a subtraction. This produces a reflection in the real-axis, which means that it is hard to see the "burning ship".

If the iteration "escapes" to large numbers, it is coloured according to how long it took to reach a cutoff point (here, 40). If it does not escape after 100 iteration, the point is coloured black.